In many problems one wants to model the relationship between a response Y and a covariate X. Sometimes it is difficult, expensive, or even impossible to observe X directly, but one can instead observe a substitute variable W which is easier to obtain. By far the most common model for the...

Considering partially linear single-index errors-in-variables model which can be described as Y = n(X T a) + ZT ßo + e when the Z' s are measured with additive errors. The general estimators established in literature are biased when ignoring the measurement errors. We proposed two estimators in...

We use ideas from estimating function theory to derive new, simply computed consistent covariance matrix estimates in nonparametric regression and in a class of semiparametric problems. Unlike other estimates in the literature, ours do not require auxiliary or additional nonparametric regressions.

Motivated by an example in nutritional epidemiology, we investigate some design and analysis aspects of linear measurement error models with missing surrogate data. The specific problem investigated consists of an initial large sample in which the response (a food frequency questionnaire, FFQ)...

There are three major points to this article: 1. Measurement error causes biases in regression fits. The line one would obtain if one could accurately measure exposure to environmental lead media will differ in important ways when one measures exposure with error. 2. The effects of measurement...

Estimating equations have found wide popularity recently in parametric problems, yielding consistent estimators with asymptotically valid inferences obtained via the sandwich formula. Motivated by a problem in nutritional epidemiology, we use estimating equations to derive nonparametric...

In this paper we consider the polynomial regression model in the presence of multiplicative measurement error in the predictor. Consistent parameter estimates and their associated standard errors are derived. Two general methods are considered, with the methods differing in their assumptions...

In many regression applications both the independent and dependent variables are measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two different nonparametric techniques, regression splines and kernel...

We describe methods for estimating the regression function nonparametrically and for estimating the variance components in a simple variance component model which is sometimes used for repeated measures data or data with a simple clustered structure. We consider a number of different ways of...

Fan, Heckman and Wand (1995) proposed locally weighted kernel polynomial regression methods for generalized linear models and quasilikelihood functions. When the covariate variables are missing at random, we propose a weighted estimator based on the inverse selection probability weights....